A dissection of the monotonicity property of binary operations from a dominance point of view

被引：0

作者：

Wang, Yuntian ^{[1
,3
]}

Zedam, Lemnaouar ^{[2
,3
]}

Hu, Bao Qing ^{[1
,4
]}

De Baets, Bernard ^{[3
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Univ Msila, Fac Math & Informat, Lab Pure & Appl Math, Rd Bordj Bou Arreridj, Msila 28000, Algeria

[3] Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure links 653, B-9000 Ghent, Belgium

[4] Guangxi Minzu Univ, Ctr Appl Math Guangxi, Sch Math & Phys, Nanning 530006, Peoples R China

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2024年 / 175卷

基金：

中国国家自然科学基金;

关键词：

Binary operation; Increasingness; Dominance relation; Lattice; AGGREGATION OPERATORS; NORMS;

D O I：

10.1016/j.ijar.2024.109304

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.

引用

页数：25

共 32 条

[1]

Alsina C, 2006, ASSOCIATIVE FUNCTIONS: TRIANGULAR NORMS AND COPULAS, P1

[2]

[Anonymous], 2002, Introduction to Lattices and Order

[3]

[Anonymous], 2003, Continuous Lattices and Domains

[4]

Baczynski M, 2008, STUD FUZZ SOFT COMP, V231, P1

[5] Three types of monotonicity of averaging functions [J].